Abstract

A dedicated 3D numerical model based on coupled mode theory and solving the rate equations has been developed to analyse, design and optimize an optical amplifier obtained by using a tapered fiber and a Er3+-doped chalcogenide microsphere. The simulation model takes into account the main transitions among the erbium energy levels, the amplified spontaneous emission and the most important secondary transitions pertaining to the ion–ion interactions. The taper angle of the optical fiber and the fiber-microsphere gap have been designed to efficiently inject into the microsphere both the pump and the signal beams and to improve their spatial overlapping with the rare earth doped region. In order to reduce the computational time, a detailed investigation of the amplifier performance has been carried out by changing the number of sectors in which the doped area is partitioned. The simulation results highlight that this scheme could be useful to develop high efficiency and compact mid-infrared amplifiers.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]

2011

2010

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

2009

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Y. G. Boucher, P. Feron, “Generalized transfer function: A simple model applied to active single-mode microring resonators,” Opt. Commun. 282, 3940–3947 (2009).
[CrossRef]

2008

2007

2006

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

2004

P. Feron, “Whispering Gallery Mode Lasers in Erbium doped fluoride glasses,” Annales de la Fondation Louis de Broglie 29, 317–329 (2004).

1999

Aggarwal, I. D.

J. S. Sanghera, I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Crystalline Sol. 256–257,6–16 (1999).
[CrossRef]

Allegretti, L.

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

Annapurna, K.

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Arnold, S.

Berneschi, S.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Boucher, Y. G.

Y. G. Boucher, P. Feron, “Generalized transfer function: A simple model applied to active single-mode microring resonators,” Opt. Commun. 282, 3940–3947 (2009).
[CrossRef]

Brenci, M.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Chen, S. Y.

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Chiasera, A.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

De Sario, M.

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

Digonnet, M. J. F.

M. J. F. Digonnet, Rare-Earth-Doper Fider Lasers and Amplifiers (Marcel Dekker Inc., 2001).
[CrossRef]

Dong, C. H.

Dumeige, Y.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Elliot, G. R.

Feron, P.

Y. G. Boucher, P. Feron, “Generalized transfer function: A simple model applied to active single-mode microring resonators,” Opt. Commun. 282, 3940–3947 (2009).
[CrossRef]

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

P. Feron, “Whispering Gallery Mode Lasers in Erbium doped fluoride glasses,” Annales de la Fondation Louis de Broglie 29, 317–329 (2004).

Ferrari, M.

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Ghisa, L.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Gorodetsky, M. L.

Grattan, K. T. V.

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Guo, G. C.

Han, Z. F.

Haus, H. A.

Hewak, D. W.

Ilchenko, V. S.

Kouki, T.

Laine, J. P.

Libchaber, A.

Little, B. E.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1988).

Makoto, T.

Mescia, L.

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

Moizan, V.

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

Murugan, G. S.

Nazabal, V.

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

Nunzi Conti, G.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Palmisano, T.

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

Panitchob, Y.

Pelli, S.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Prudenzano, F.

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

Ren, H. C.

Righini, G. C.

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Sanghera, J. S.

J. S. Sanghera, I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Crystalline Sol. 256–257,6–16 (1999).
[CrossRef]

Sebastiani, S.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

Sen, R.

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Senthil Murugan, G.

Smektala, F.

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1988).

Stephen, A.

F. Vollomer, A. Stephen, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

Sun, T.

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Vahala, K.

K. Vahala, Optical Microcavities (World Scientific Publishing, 2004).
[CrossRef]

Vahala, K. J.

Vollmer, F.

Vollomer, F.

F. Vollomer, A. Stephen, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

Wilkinson, J. S.

Wu, X. W.

Xiao, Y. F.

Yang, L.

Yang, Y.

Zervas, M. N.

Zou, C. L.

Annales de la Fondation Louis de Broglie

P. Feron, “Whispering Gallery Mode Lasers in Erbium doped fluoride glasses,” Annales de la Fondation Louis de Broglie 29, 317–329 (2004).

IEEE Photon. Techonol. Lett.

L. Mescia, F. Prudenzano, M. De Sario, T. Palmisano, M. Ferrari, G. C. Righini, “Design of Rare-Earth-Doped Microspheres,” IEEE Photon. Techonol. Lett. 22, 422–424 (2010).
[CrossRef]

J. Lightwave Technol.

J. Non-Crystalline Sol.

G. Nunzi Conti, A. Chiasera, L. Ghisa, S. Berneschi, M. Brenci, Y. Dumeige, S. Pelli, S. Sebastiani, P. Feron, M. Ferrari, G. C. Righini, “Spectroscopic and lasing properties of Er3+ doped glass microspheres,” J. Non-Crystalline Sol. 352, 2360–2363 (2006).
[CrossRef]

J. S. Sanghera, I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Crystalline Sol. 256–257,6–16 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Methods

F. Vollomer, A. Stephen, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[CrossRef]

Opt. Commun.

Y. G. Boucher, P. Feron, “Generalized transfer function: A simple model applied to active single-mode microring resonators,” Opt. Commun. 282, 3940–3947 (2009).
[CrossRef]

S. Y. Chen, T. Sun, K. T. V. Grattan, K. Annapurna, R. Sen, “Characteristics of Er and ErYbCr doped phosphate microsphere fibre lasers,” Opt. Commun. 282, 3765–3769 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Mat.

F. Prudenzano, L. Mescia, L. Allegretti, V. Moizan, V. Nazabal, F. Smektala, “Theoretical study of cascade laser in erbium-doped chalcogenide glass fibers,” Opt. Mat. 33, 241–245 (2010).
[CrossRef]

Other

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall Inc., 1984).

M. J. F. Digonnet, Rare-Earth-Doper Fider Lasers and Amplifiers (Marcel Dekker Inc., 2001).
[CrossRef]

K. Vahala, Optical Microcavities (World Scientific Publishing, 2004).
[CrossRef]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1988).

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Figures (11)

Fig. 1
Fig. 1

Layout scheme of the fiber taper coupled to the Er3+-doped chalcogenide micro-sphere.

Fig. 2
Fig. 2

Energy level diagram of the Er3+ ions considered in our simulations.

Fig. 3
Fig. 3

Discretization of the doped area in the plane r̂ ·θ̂.

Fig. 4
Fig. 4

Transmission spectrum of the undoped microsphere, having radius R0 = 25 μm, around (a) pump wavelength λp = 0.98 μm and (b) signal wavelength λs = 2.76 μm.

Fig. 5
Fig. 5

Signal transmittance versus the number of the sector q for different maximum polar angles: θmax = π/5 rad (full curve), θmax = π/10 rad (dash curve), θmax = π/20 rad (dash-dot curve) and θmax = π/30 rad (dot curve).

Fig. 6
Fig. 6

Signal transmittance versus the thickness of the doped region s for different maximum polar angles: θmax = π/5 rad (full curve), θmax = π/10 rad (dash curve), θmax = π/20 rad (dash-dot curve) and θmax = π/30 rad (dot curve).

Fig. 7
Fig. 7

Signal transmittance versus the maximum polar angle for different thicknesses of the doped region: s=3 μm (full curve), s=2 μm (dash curve), and s=1 μm (dot curve).

Fig. 8
Fig. 8

Transmittance versus the fibre-microsphere gap for different erbium concentrations: NEr = 0.5 w% (full curve), NEr = 0.3 w% (dash curve), and NEr = 0.1 w% (dot curve); transmittance of the undoped microsphere at pump wavelength (square mark) and at signal wavelength (circular mark).

Fig. 9
Fig. 9

Signal transmittance versus the fibre-microsphere gap for different taper angles: δ = 0.01 rad (full curve), δ = 0.02 rad (dash curve), and δ = 0.03 rad (dot curve).

Fig. 10
Fig. 10

Signal transmittance versus the pump power for different input signal powers: Ps = −50 dBm (full curve), Ps = −40 dBm (dash curve), and Ps = −30 dBm (dot curve).

Fig. 11
Fig. 11

Signal transmittance versus the time for different input pump powers: Pp = 200 mW (full curve), Pp = 100 mW (dash curve), and Pp = 50 mW (dot curve).

Tables (1)

Tables Icon

Table 1 Spectroscopic parameters of the Er3+-doped chalcogenide microsphere.

Equations (29)

Equations on this page are rendered with MathJax. Learn more.

1 r 2 sin θ [ sin θ r ( r 2 ψ r ) + θ ( sin θ ψ θ ) + 1 sin θ 2 ψ φ 2 ] + k 2 n s 2 ψ = 0
( η s α s + l R 0 ) j l ( k n s R 0 ) = k n s j l + 1 ( k n s R 0 )
η s = { 1 TEmode n s 2 n 0 2 TMmode α s = β l 2 k 2 n 0 2 β l = l ( l + 1 ) R 0
d A l , m , n d t = 1 2 ( 1 τ ext + 1 τ 0 2 i Δ ω ) A l , m , n + i 1 τ ext τ A in
K f s = V k 2 ( n s 2 n 0 2 ) 2 β f E f E s * d V
0 π 0 + | E f | 2 r d r d θ = 1
0 π 0 + | E s | 2 r d r d θ = 1
a ( z ) = a 0 + | z | δ
k f J 1 [ a ( z ) k f ] J 0 [ a ( z ) k f ] = α f K 1 [ a ( z ) α f ] K 0 [ a ( z ) α f ]
k f = k 2 n f 2 β f 2
α f = β f 2 k 2 n 0 2
d N 1 q d t = ( W 21 q + C up N 2 q + C 24 N 4 q + A 21 ) N 2 q + ( C 3 N 3 q + A 31 ) N 3 q + A 41 N 4 q + A 51 N 5 q + A 61 N 6 q + ( R 13 q + R 14 q + W 12 q + 2 C 16 N 6 q + C 14 N 4 q ) N 1 q
d N 2 q d t = ( W 12 q + 2 C 16 N 6 q + C 14 N 4 q ) N 1 q + ( W 32 q + A 32 ) N 3 q + ( C 14 N 1 q + C 4 N 4 q + A 42 ) N 4 q + A 52 N 5 q + + A 62 N 6 q ( W 21 q + C 24 N 4 q + 2 C up N 2 q + A 21 ) N 2 q
d N 3 q d t = R 13 q N 1 q + A 43 N 4 q + A 53 N 5 q + A 63 N 6 q ( W 32 q + 2 C 3 N 3 q + A 31 + A 32 ) N 3 q
d N 4 q d t = 2 C 16 N 1 q N 6 q + C up ( N 2 q ) 2 ( A 41 + A 42 + A 43 + C 14 N 1 q + 2 C 4 N 4 q + C 24 N 2 q ) N 4 q + + A 54 N 5 q + A 64 N 6 q + R 14 q N 1
d N 5 q d t = A 65 N 6 q ( A 51 + A 52 + A 53 + A 54 ) N 5 q
d N 6 q d t = C 3 ( N 3 q ) 2 + C 4 ( N 4 q ) 2 + C 24 N 2 q N 4 q ( A 61 + A 62 + A 63 + A 64 + A 65 + 2 C 16 N 1 q ) N 6 q
R i j q = l , m , n R i j q , l , m , n
W i j q = l , m , n W i j q , l , m , n
R i j q , l , m , n = σ i j ( ν ˜ ) h ν ˜ S q S q I l , m , n p ( r , θ , φ = 0 , t ) r d r d θ
W i j q , l , m , n = σ i j ( ν ˜ ) h ν ˜ S q S q I l , m , n s ( r , θ , φ = 0 , t ) r d r d θ
I l , m , n a ( r , θ , φ , t ) = 1 2 ɛ 0 c n eff ( ν ˜ ) | A l , m , n a ( φ , t ) | 2 | E l , m , n a ( r , θ ) | 2 with a = p , s
R i j q , l , m , n = σ i j ( ν ˜ ) 2 ν ˜ h S q ɛ 0 c n eff ( ν ˜ ) | A l , m , n p ( φ = 0 , t ) | 2 Γ l , m , n q , p
W i j q , l , m , n = σ i j ( ν ˜ ) 2 ν ˜ h S q ɛ 0 c n eff ( ν ˜ ) | A l , m , n s ( φ = 0 , t ) | 2 Γ l , m , n q , s
Γ l , m , n q , a = S q | E l , m , n q ( r , θ ) | 2 rdrd θ with a = p , s
d A l , m , n p d t = c 2 n eff [ q N j q σ j i ( ν ˜ ) Γ l , m , n q , p q N i q σ i j ( ν ˜ ) Γ l , m , n q , p ] A l , m , n p with i < j d A l , m , n s d t = c 2 n eff { q N j q σ j i ( ν ˜ ) Γ l , m , n q , s [ A l , m , n s + A 0 ] q N i q σ i j ( ν ˜ ) Γ l , m , n q , s A l , m , n s } with i < j
d A l , m , n p d t = 1 2 ( 1 τ ext + 1 τ 0 g l , m , n p 2 i Δ ω ) A l , m , n p + i 1 τ ext τ A in , l , m , n p d A l , m , n s d t = 1 2 ( 1 τ ext + 1 τ 0 g l , m , n s 2 i Δ ω ) A l , m , n s + c 2 n eff q N j q σ j i ( ν ˜ ) Γ l , m , n q , s A 0 + + i 1 τ ext τ A in , l , m , n s
g l , m , n q = c n eff ( q N j q σ j i ( ν ˜ ) Γ l , m , n q , a q N i q σ i j ( ν ˜ ) Γ l , m , n q , a ) with a = p , s
T = | A out , l , m , n a A in , l , m , n a | 2 = | 1 τ τ ext + i τ τ ext A l , m , n a A in , l , m , n a | with a = p , s

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